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conditional

DOI:
10.1111/b.9781405106795.2004.x

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L ogic A conditional, or a conditional statement, is a complex sentence of the form: “if p then q.” Both p and q are statements, with p the antecedent and q the consequent. The logical relation between the antecedent and consequent is called implication. The converse of the conditional, that is, “if not q then not p,” is called the contrapositive. Conditionals are also called hypotheticals. In propositional logic, a conditional is generally symbolized as “p→q” or “p⊃q.” The major problem associated with conditionals is determining their truth condition . Most commonly a conditional is treated as a truthfunction such that “if p then q” is false if and only if p is true and q is false. This is called the material conditional or material implication. But there is a paradox associated with the material conditional that has led to a revision called the strict conditional, which claims that a conditional is true if and only if when p is true, q is necessarily true. There are, however, also problems associated with strict conditionals . A much-debated issue concerns the truth conditions of the counterfactuals in which the antecedent is false. For example, “If Kennedy had not been killed, he would have won the next election.” The problem of counterfactuals is also closely associated with the discussion of possible worlds. “A sentence of the form ‘If … then …’, where the blanks ... log in or subscribe to read full text

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